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Selection of fixed effects in high dimensional linear mixed models using a multicycle ECM algorithm

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  • Rohart, Florian
  • San Cristobal, Magali
  • Laurent, Béatrice

Abstract

Linear mixed models are especially useful when observations are grouped. In a high dimensional setting however, selecting the fixed effect coefficients in these models is mandatory as classical tools are not performing well. By considering the random effects as missing values in the linear mixed model framework, a ℓ1-penalization on the fixed effects coefficients of the resulting log-likelihood is proposed. The optimization problem is solved via a multicycle Expectation Conditional Maximization (ECM) algorithm which allows for the number of parameters p to be larger than the total number of observations n and does not require the inversion of the sample n×n covariance matrix. The proposed algorithm can be combined with any variable selection method developed for linear models. A variant of the proposed approach replaces the ℓ1-penalization with a multiple testing procedure for the variable selection aspect and is shown to greatly improve the False Discovery Rate. Both methods are implemented in the MMS R-package, and are shown to give very satisfying results in a high-dimensional simulated setting.

Suggested Citation

  • Rohart, Florian & San Cristobal, Magali & Laurent, Béatrice, 2014. "Selection of fixed effects in high dimensional linear mixed models using a multicycle ECM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 209-222.
    • Handle: RePEc:eee:csdana:v:80:y:2014:i:c:p:209-222
    DOI: 10.1016/j.csda.2014.06.022
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    References listed on IDEAS

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    3. Mammen, Enno & Wilke, Ralf A. & Zapp, Kristina Maria, 2022. "Estimation of group structures in panel models with individual fixed effects," ZEW Discussion Papers 22-023, ZEW - Leibniz Centre for European Economic Research.
    4. Ollier, Edouard & Samson, Adeline & Delavenne, Xavier & Viallon, Vivian, 2016. "A SAEM algorithm for fused lasso penalized NonLinear Mixed Effect Models: Application to group comparison in pharmacokinetics," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 207-221.
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    7. Caroline Bazzoli & Sophie Lambert-Lacroix & Marie-José Martinez, 2023. "Partial least square based approaches for high-dimensional linear mixed models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 769-786, September.

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